Not linking back is a major pain in all linkups and even when there are such rules, entrants continuously break them.

Since linkup should be beneficial to both hosts and participants, hosts usually require a link back. A link on the participants' site to link back to the linkup site.
This is usually enforced manually. If someone has many links though, it is usually impossible to visit all the linked sites to see that they indeed have a link back and, if not, go back to the moderation page and delete the link.

This is where InLinkz comes to play with the backlink option to help you build your incoming links by requiring backlinks from your entrants to your blog.
Make sure the entrants can leave their link in your collection only if they follow your rules.

This backlink acts as a good referral from other blogs so it is beneficial to your PageRank.

Here is how you can require backlinks to your blog:

1. Click to expand the +Advanced options while creating or editing a link party.

2. Enable the "Require backlinks" option.

3. Once you enable it, the blog(s) you have associated with your Inlinkz account will be displayed. The reader's links should point to this URL/ these URLs.

Note: To set or change the URLs you have associated with your blog, go to your Settings > My Blogs.

When entrants submit links that Inlinkz is unable to verify their backlinks, the system will still add them to the collection but they will not be displayed on hosts' blog until they moderate them.
The hosts will receive an email about the pending for moderation links and as soon as they approve them from their dashboard > Manage links, the links will be displayed in their collection.

If you have enabled the require backlinks option from the +Advanced options, then, each time an entrant submits a link that doesn't comply with this ruleset,
the link won't be displayed in your collection until you moderate it.

Once you approve that link, it will be displayed normally in your party. If you reject it, it will be deleted from your collection permanently.

If the host of a link party asks for a backlink in order to be allowed to add your link to the party, you need to have a plain HTML link from your blog to the host's blog.

When the backlink option is enabled, the following message pops up on the linking page to notify you where exactly you have to link back.

If you are asked e.g. to backlink to fresh.inlinkz.blog.com, you should have a link that leads there somewhere in your blog post. This, in HTML looks something like this:
<A HREF=http://www.fresh.inlinkz.blog.com>Backlink to fresh.inlinkz.blog</A>

Usually, hosts that require a backlink, provide a way to grab easily the code from their site in the form of a button, so just grab their button and put it in your blog post.